# Paired t-Test of Means

Where $\bar x_1$ and $\bar x_2$ are the two means, and $s_{{\bar x_1} - {\bar x_2}}$ is an estimate of the Standard Error of the difference between the means:

$t=\frac{\bar x_1-\bar x_2}{s_{{\bar x_1} - {\bar x_2}}}$

where

$p \approx 2\Pr(t_{n-1} \ge |t|)$,
$n$ is the sample size,
$s_{{\bar x_1} - {\bar x_2}}$ is computed as the Standard Error of $d$,
the value for the $i$th observation is computed as $d_i = x_{i1} - x_{i2}$ where $x_1,x_2$ are the observed values on the two variables.